Angular Acceleration

This work has been performed to verify the existent knowledge on determination of the mass moment. For the experiment, a compound pendulum was used. The motivation to undertake these studies were experimental results indicating a big discrepancy in mass moments between the values coming from calculations using the definition formula and these obtained from the experiment. In relation to the axial moment the relative error equals 23.6%, whereas regarding the polar moment the error reached 56.4%. Considering the reason of that discrepancy we could find the existent theory not to be adequate. The theory is then considered in view of verifying first the mathematical pendulum and next the physical/compound pendulum theory. The consideration has been focused on the description of accelerated motion cycle of both pendulums as it was enough to solve the problem. A source differential equation, which serves to solve any quantum phenomena, was used in the study. Then the course of creation of...

Abstract: This paper presents an extended Kalman filter for real-time estimation of rigid body orientation using the newly developed MARG (Magnetic, Angular Rate, and Gravity) sensors. Each MARG sensor contains a three-axis magnetometer, a three-axis angular rate sensor, and a three-axis accelerometer. The filter represents rotations using quaternions rather than Euler angles, which eliminates the long-standing problem of singularities associated with attitude estimation. A process model for rigid body angular motions and angular rate measurements is defined. The process model converts angular rates into quaternion rates, which are integrated to obtain quaternions. The Gauss-Newton iteration algorithm is utilized to find the best quaternion that relates the measured accelerations and earth magnetic field in the body coordinate frame to calculated values in the earth coordinate frame. The best quaternion is used as part of the measurements for the Kalman filter. As a result of this a...

In this paper the adaptive control of a 2 degrees of freedom (DOF) classical mechanical system, a ball-beam system is considered. The control task has the interesting feature that only one of the DOFs of the system, i.e. the position of the ball is controlled via controlling the other axis, the tilting angle of the beam. Since the acceleration of the ball rolling on the beam depends on the gravitation and the tilting angle of the beam, and due to the phenomenology of classical mechanical systems the directly controllable physical quantity is the rotational acceleration of the beam, this system is a 4th order one because it is the 4th time-derivative of the ball's position that can directly be influenced by the control. Another interesting feature of this system is its "saturation" since the rotational angle of the beam must be limited within the interval (-90deg, +90deg) that also sets limits to the available acceleration of the ball. In the present approach a feedback control is applied in which the above limitation is achieved by the application of an angular potential and an angular velocity potential. Utilizing the fact that the partial derivative of the 4th time-derivative of the ball's position according to the angular acceleration of the beam has a well defined sign, a single tuneable adaptive parameter is introduced that does not represent the parameters of the system under control. The control is illustrated via simulation results

Abstract It is shown that the angular acceleration and velocity of a rigid body can be determined from translational material acceleration measurements made by an observer on the body. An important contribution is the fact is that this can be done without integration. ...